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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2512.14573 |
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| _version_ | 1866914204342026240 |
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| author | Banerjee, Arindam Ha, Tai Huy Lama, Vivek Bhabani |
| author_facet | Banerjee, Arindam Ha, Tai Huy Lama, Vivek Bhabani |
| contents | We introduce and study the defect function associated to a pair of filtrations of ideals, which generalizes the symbolic defect of ideals. Under the assumption that the Rees algebra of one filtration is Noetherian and that a natural graded module measuring the interaction between the filtrations is finitely generated over it, we show that the corresponding defect function is asymptotically a quasi-polynomial. Moreover, the defect function becomes eventually polynomial when the Rees algebra of the first filtration is standard graded. For filtrations arising from saturations and ordinary powers of monomial ideals, we further analyze the structure of the quasi-polynomial. We prove that the top two coefficients of the eventual quasi-polynomial are constant under natural hypotheses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Defect Functions Between Filtrations of Ideals Banerjee, Arindam Ha, Tai Huy Lama, Vivek Bhabani Commutative Algebra 13A02, 13A15 We introduce and study the defect function associated to a pair of filtrations of ideals, which generalizes the symbolic defect of ideals. Under the assumption that the Rees algebra of one filtration is Noetherian and that a natural graded module measuring the interaction between the filtrations is finitely generated over it, we show that the corresponding defect function is asymptotically a quasi-polynomial. Moreover, the defect function becomes eventually polynomial when the Rees algebra of the first filtration is standard graded. For filtrations arising from saturations and ordinary powers of monomial ideals, we further analyze the structure of the quasi-polynomial. We prove that the top two coefficients of the eventual quasi-polynomial are constant under natural hypotheses. |
| title | Defect Functions Between Filtrations of Ideals |
| topic | Commutative Algebra 13A02, 13A15 |
| url | https://arxiv.org/abs/2512.14573 |